I think a lot of this is not about the shower, really.
You see the house as yours, because you paid the mortgage. All landlords have paid/are paying the mortgage on their properties; but when they are rented out they are not their homes.
Your daughter might be asserting herself as a renter by doing the 'my house/my rules' thing. That isn't (to me) unreasonable. You are effectively a guest in her flat, whether you like it or not, and guests don't call the shots, particularly when they haven't been invited (sorry).
What does your partner have to say about his? You say that the situation is causing problems in your relationship with him, which suggests that he has an opinion on it all.
It is fairly easy to resolve, really; but it would mean accepting that the flat is yours in name only, so long as someone is paying you rent.
If you ask your daughter to find another flat and rent yours to someone else, there will be no issue, as you would not be allowed to stay there. This might alienate your daughter, though, and you would need to consider if doing that is worth it for a couple of weeks a year.
If you stay in a hotel/b&b when you are in the UK, your daughter would have the quiet enjoyment of her space that she is paying for.
If she is paying below the market rate, she could maybe find a flatmate and share the rent. If they agreed on the use of the facilities and put it in the contract, that could be a solution, and she would learn that compromise is sometimes necessary.
If that wouldn't work, you could increase the rent in small doses, so that she isn't immediately priced out.
Honestly, as you spend most of your time abroad, do you want to risk souring your relationship with your daughter (and maybe your partner) over an occasional visit?
Alphabetical girls and boys names January 2024